# Markov type bound based on KL divergence?

Given two discrete distribution $$p, q$$ on some universe $$U$$, if I know they have a bounded KL divergence, say some number $$c$$, can I say anything about how much each point in the universe differs in probability?

The statement can be like, for $$1\%$$ of the probability mass (in terms of $$p$$), $$p(x)/q(x)$$, is somewhere between $$2^{-c}$$ and $$2^c$$, or at least $$2^{-c}$$, or at most $$2^{c}$$. Any conclusion along this line is good. And any constant here can be changed.

• I think you may be interested in the idea of a typical set. – mhdadk Mar 23 at 21:35